function extensionality (changes)

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Remember that when two functions $f,g : A \to B$ are homotopic we have a witness to

$\prod_{x : A} f(x)=g(x)$

but as discussed in the homotopy article, it is not the case that $f=g$.

Function extensionality simply assumes this is the case as an axiom.

The axiom of functional extensionality says that for all $A,B$, $f,g : A \to B$ there is a function

$funext : (f \sim g) \to (f = g)$

This allows homotopic functions to be equal.

category: axioms, type theory

Created on October 11, 2018 at 08:58:24. See the history of this page for a list of all contributions to it.